Improving molecular orientation by optimizing relative delay and intensities of two-color laser pulses

We numerically explore molecular orientation dynamics with moderately intense nanosecond two-color laser pulses. It is believed that the nanosecond two-color pulse can adiabatically control the molecular orientation. However, in our simulation based on the time-dependent Schrödinger equation, which naturally includes nonadiabatic effects, the orientation dynamics shows clear deviations from the adiabatic approximation (AA) results, while the molecular alignment dynamics is in good agreement with the AA results. The nonadiabaticity is significantly influenced by three parameters, the intensities, and the relative delay of the two wavelengths. In this work, we clarify the reason behind the nonadiabaticity and provide the solutions for achieving higher degrees of orientation.

Figure 1

Molecular alignment and orientation.

Figure 2

Temporal profiles of two-color laser pulses. Right and left panels illustrate the two-color laser pulses with and without a delay between the two wavelengths. The two-color laser pulses with the optimal delay can give rise to higher degrees of orientation than those with the zero delay.

Figure 3

The degrees of orientation (left) and alignment (right) observed at the peak of the $2\omega$ pulse. The horizontal axis is the peak intensity of the $\omega$ pulse, while the vertical axis is the delay between the $\omega$ and $2\omega$ pulses. The peak intensity of the $2\omega$ pulse is fixed at either $8.0\times {10}^{10}{\mathrm{W}/\mathrm{cm}}^2$ (1) or $6.0\times {10}^{11}{\mathrm{W}/\mathrm{cm}}^2$ (2). The TDSE and AA results are shown.

Figure 4

Temporal evolutions of the degrees of orientation and alignment (left) and the populations of the two lowest-lying pendular states (right). In the left panels, the left vertical axis of each panel represents $\langle cos\theta \rangle$ or $\langle {cos}^2\theta \rangle$, while the right vertical axis of each panel represents the intensities of the $\omega$ and the $2\omega$ pulses in units of ${10}^{11}{\mathrm{W}/\mathrm{cm}}^2$. In the right panels, the left vertical axis represents the populations of the two lowest-lying pendular states, while the right vertical axis of each panel represents the intensities of the $\omega$ and the $2\omega$ pulses in units of ${10}^{11}{\mathrm{W}/\mathrm{cm}}^2$. The four different conditions labeled by (a), (b), (c), and (d) in Fig. 3 are employed.

Figure 5

Schematic illustrations of the orientation processes. The upper path shows a nonadiabatic orientation process, for which the orientation is preceded by the strong adiabatic alignment. The lower path shows an adiabatic orientation process, which could be achieved by forming the alignment and orientation potentials in harmony with each other.

Figure 6

Temporal evolutions of the degrees of orientation and alignment (left) and populations of two lowest-lying pendular states (right). In the left panels, the left vertical axis of each panel represents $\langle cos\theta \rangle$ or $\langle {cos}^2\theta \rangle$, while the right vertical axis of each panel represents the intensities of the $\omega$ and the $2\omega$ pulses in units of ${10}^{11}{\mathrm{W}/\mathrm{cm}}^2$. In the right panels, the left vertical axis represents the populations of the two lowest-lying pendular states, while the right vertical axis of each panel represents the intensities of the $\omega$ and the $2\omega$ pulses in units of ${10}^{11}{\mathrm{W}/\mathrm{cm}}^2$. The conditions labeled by (${\mathrm{a}}^{\prime }$), (${\mathrm{b}}^{\prime }$), (${\mathrm{c}}^{\prime }$), (${\mathrm{d}}^{\prime }$), and (${\mathrm{e}}^{\prime }$) in Fig. 3 are employed. For the (${\mathrm{d}}^{\prime }$) and (${\mathrm{e}}^{\prime }$) cases, the evolving rotational binding potentials are also illustrated.

Figure 7

Time evolutions of the degrees of orientation (left) and alignment (right) of thermal molecular ensembles in the four different rotational temperatures. The solid lines are the results from the TDSE, while the dotted lines are those from the AA. The right vertical axis of each panel represents the intensities of the $\omega$ and the $2\omega$ pulses in units of ${10}^{11}{\mathrm{W}/\mathrm{cm}}^2$. The conditions labeled by (${\mathrm{a}}^{\prime }$), (${\mathrm{b}}^{\prime }$), (${\mathrm{c}}^{\prime }$), (${\mathrm{d}}^{\prime }$), and (${\mathrm{e}}^{\prime }$) in Fig. 3 are employed.

Figure 8

The degrees of orientation (left) and alignment (right) of the rotational ground state of an OCS molecule. The horizontal and vertical axes are the peak intensities of $\omega$ and $2\omega$ pulses, respectively. The delay between the two pulses is set at zero ns. The TDSE and AA results are shown.